The system of equations are  

Write the equations into matrix form ,

where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations in Gauss-Jordan method.

The augmented matrix is .

.

The augmented matrix is .

Apply elementary row operations to obtain a reduced row-echelon form.

Let are represents first row, second row and third row.

Therefore the solutions of the augmented matrix are and .

The solution matrix is .

The solution matrix is .